Particularly means especially or more than usual. When your teacher says she's particularly proud of how hard you worked on your science project, she means she's extra proud, beyond her normal level of pride. When someone mentions they're particularly good at chess, they're highlighting chess as a special strength.

The word draws attention to something specific within a larger group. If you say “I like all vegetables, particularly carrots,” you're saying carrots stand out as your favorite. If a coach says “Everyone played well today, particularly the defense,” she's giving the defensive players special recognition while still acknowledging the whole team.

Particularly adds emphasis and precision to your meaning. Compare “It was hot yesterday” to “It was particularly hot yesterday.” The second version tells your listener that yesterday's heat was noteworthy, maybe even unusual. You can use particularly to make your speaking and writing more exact: instead of saying “I'm interested in history,” you might say “I'm particularly interested in the history of ancient Rome,” which gives people a much clearer picture of what fascinates you.